Given that the vector å = a,î + a2j + azk and b = b,î + b2j + b3k. Show that the vector product of å and b can be expressed as a determinant. %3D

Q: Use a determinant to find the area of the triangle with the given vertices

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Q: Using the property of determinants, prove that |1 bc a(b+c)| 1 1 ab c(a+ b)| 2) ca b(c +a)| = 0

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Q: The set S is called a spanning set of V if the determinant is a. zero b. negative numbers c.…

A: Solution

Q: Find the value of the determinant D given by: a D =c d -5 2 4 3 where a = 4, b = 4, c = 7, d = 13

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Q: Find the value of the determinant D given by: 1. 1 1 D = b a a b c2 where a = 7, b = 16 and C = -6…

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Q: A = 5 -2 -5 1 a b C d - 2 1 -3 1 1 -2 9 4

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Q: - Fill in the blanks with appropriate numbers to calculate the determinant. Where there is "±",…

A: det21-34Find the matrix determinant according to formula:  deta  b c  d  = ad-bc=2· 4-1·-3=11

Q: If A = 4 3    and      B = 2 -5         -1 -2                    -1 -2 Find:- a) A2   b)…

A: Matrix and determinants

Q: Verify the identity by expanding each determinant.

A: abcd+abef=abc+ed+f

Q: If ∣A∣ = 7 and A is of order 4, then find each determinant.(a) ∣3A∣ (b) ∣AT∣ (c) ∣A−1∣ (d) ∣A3∣

A: Here given Use the property of determinant which states that

Q: If A and B are 3 × 3 matrices and |A| = -3,|B| = 2, com- pute the following determinants. (a) |AB|…

A: Given A and B are a 3×3 matrix with A=-3 and B=2. a We have to compute AB. Use property of…

Q: Verify the identity by expanding each determinant.

A: given akbckd=kabcdverify the identity by expanding the each determinant.

Q: Find the determinant in a) and b) where га CT f il det d e 7 %3D Lg_h а b C а C] а) А- 15g d f 5h…

A: Following are some results concerning determinant of a matrix. If we interchange any two rows, then…

Q: Find the determinant of the vector A = 2i+ 5j + 6k and B = 8k

A: determinant is nothing but finding the cross product. so, determinant of two vectors A and B = A×B

Q: If [B] = [A][A], What is the determinant of [B] given that [A] = %3D B| = 4 B = 16 B| = 9 B| = -4

A: The given matrix is A=2302. It is given that [B]=[A][A]. Evaluate the matrix B as follows.…

Q: a) By using the property of the determinants prove that 1 + a? - b2 2ab -2b 1- a? + b? = (1 + a? +…

A: By using the properity of determinats prove that :

Q: Let a, b e R. (a) Find the determinant of -2 1 -2 - 2.

A: (a) Given that, a2b-2124-2-1

Q: Evaluate the determinants to verify the equation.

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Q: Verify the identity by expanding each determinant.

A: Given- abcd=-badc To verify- The identity by expanding determinant.

Q: c. Given that the vector à = a,î + azĵ + azk and b = b,î + b2ĵ + bzk. Show that the vector product…

A: Given:     a→=a1i+a2j+a3k     b→=b1i+b2j+b3k  The vector product of two vectors  a→=a1i+a2j+a3k and…

Q: Find the determinants in Exercise , assuming that

A: Determinant is used for solving linear equations. To find the inverse of a matrix determinant is…

Q: Verify the identity by expanding each determinant.

A: We have to prove that, abcd=abka+ckb+d

Q: If B = then the determinant of B~1 is_ - (use property) a. 2 d. b. 10 с. 0.5

A: A matrix is a quantity with rows and columns. An entry in a matrix is determined by its row number…

Q: Find the vector, not with determinants, but by using properties of cross products. k x (i - 2j)

A: The product of the vector helps to find the required product. The answer to the product is whereas…

Q: Let A be a 5 x 5 matrix and JA| = 3. The determinant of 2A is equal to (A) 96 (в) 48 c) 32 (D 6

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Q: Find the area of a triangle with given vertices using determinants: A(0,0), B(3,1) and C(1,5) 8 5 7…

A: This question is based on finding area of triangle using determinant.

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: The given determinant is  ijk1-2321-4.

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: Given determinant: ijk4-62-23-1

Q: If A =     4   2     and   B =    1    -3               5   7                        0    -2 Find…

A: Given matrix

Q: Find the values of 1 for which the determinant is zero. (Enter your answers as a comma-separated…

A: finding determinant by using first column

Q: If A =     2   1     and   B =    2    -3                   8   6                      -1    -2…

A: We have A=2    18    6,B=2     -3-1    -2

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: To express the determinant in the form of ai+bj+ck for real numbers a,b,c. ijk5-6-1301 Solution:…

Q: Sketch the triangle with the given vertices, and use a determinant to find its area. (1, 0), (3, 5),…

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Q: By using the properties of determinant prove that a? |b² + c² b² a? c2 + a? b2 4a?b?c? c2 c2 a² + b²

A: By using the determinant property that is:…

Q: Verify the identity by expanding each determinant.

A: We have to verify the identity by expanding each side of determinants: abcd=aka+bckc+d Taking LHS,…

Q: If A =     4   3     and   B =    2    -5             -1   -2                      -1    -2 Find:-…

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Q: If A = 3 -5 and B = 6 -3           3 2                4 -1 Find:- a) A*A b) determinant A c) adjoint…

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Q: Find the determinants in Exercises, where d f= 7 a

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Q: a +d b+e c+, Find the determinants in Exercises, where d

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Q: 1) If A = 2 1 and B = 2 -3 8 6 -1 -2 Find:- a) BA b) determinant B c) Adjoint B d) A1

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Q: In a mechanical system, acceleration a, velocity v, and distance S, are related by the simultaneous…

A: a. Using the coefficient of the variables, the main determinant for the given system of equations…

Q: Express the determinant in the form ai + bj + ck for real numbers a, b, and c.

A: To: Express the determinant in the form ai + bj + ck for real numbers a, b, and c. ijk2-16-351

Q: Verify the identity by expanding each determinant.

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Q: Ja + b а а a + b — b? (За + b) а а %3D а а + bl а

A: Let…

Q: Let - (3) and Compute the area of the parallelogram determined by ū, i, ủ + 0, 0, and compute the…

A: We have to find the area of parallelogram.

Q: B(4,7) Cl9,5) 4 3 JA(1,2) 2 3 5 6 1 8 9

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Q: Use a determinant to find the area of the triangle with the given vertices. (-6, 0), (6, 0), (0, 3)

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: If A= () B= () c= () 36 53 Then the determinant of C =

A: Solved below

Q: Show that the equation of a line through (x1, yı) and (x2, y2) is given by the following…

A: A determinant